Sparse Estimation Strategies in Linear Mixed Effect Models for High-Dimensional Data Application |
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Authors: | Eugene A Opoku Syed Ejaz Ahmed Farouk S Nathoo |
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Institution: | 1.Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8P 5C2, Canada;2.Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S 3A1, Canada; |
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Abstract: | In a host of business applications, biomedical and epidemiological studies, the problem of multicollinearity among predictor variables is a frequent issue in longitudinal data analysis for linear mixed models (LMM). We consider an efficient estimation strategy for high-dimensional data application, where the dimensions of the parameters are larger than the number of observations. In this paper, we are interested in estimating the fixed effects parameters of the LMM when it is assumed that some prior information is available in the form of linear restrictions on the parameters. We propose the pretest and shrinkage estimation strategies using the ridge full model as the base estimator. We establish the asymptotic distributional bias and risks of the suggested estimators and investigate their relative performance with respect to the ridge full model estimator. Furthermore, we compare the numerical performance of the LASSO-type estimators with the pretest and shrinkage ridge estimators. The methodology is investigated using simulation studies and then demonstrated on an application exploring how effective brain connectivity in the default mode network (DMN) may be related to genetics within the context of Alzheimer’s disease. |
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Keywords: | linear mixed model ridge estimation pretest and shrinkage estimation multicollinearity asymptotic bias and risk LASSO estimation high-dimensional data |
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